Question
Find the GCF. \( x^{5} y^{8}, x^{6} y^{6}, x^{4} y^{7},-x^{3} y^{3} \) The GCF is \( \square \).
Ask by Smith Wheeler. in the United States
Feb 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The GCF is \( x^{3} y^{3} \).
Solution
To find the Greatest Common Factor (GCF) for a set of monomials, we look at each variable separately and take the smallest exponent in which it appears.
The monomials are:
• x⁵y⁸
• x⁶y⁶
• x⁴y⁷
• –x³y³
1. For x: The exponents are 5, 6, 4, and 3. The smallest exponent is 3.
2. For y: The exponents are 8, 6, 7, and 3. The smallest exponent is 3.
Thus, the GCF is x³y³.
The GCF is □ = x³y³.
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Simplify this solution Bonus Knowledge
To find the GCF of the terms \( x^{5}y^{8}, x^{6}y^{6}, x^{4}y^{7}, -x^{3}y^{3} \), we look at the lowest power of each variable across all terms. For \( x \), the smallest exponent is 3 (from \( -x^{3}y^{3} \)), and for \( y \), the smallest exponent is 3 (also from \( -x^{3}y^{3} \)). Therefore, the GCF is \( x^{3}y^{3} \). So, the GCF is \( x^{3} y^{3} \).
